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Square Reciprocal Summation (Posted on 2020-08-25) Difficulty: 3 of 5
{3,3,3,3,3,3} is a set of six integers such that the sum of the squares of the reciprocals totals 2/3.
(1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 + (1/3)^2 = 2/3

Does there exist a set of integers with fewer than 6 members whose sum of the squares of the reciprocals totals 2/3?

Problem inspired by Find the triplets

No Solution Yet Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

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soln | Comment 1 of 5
computer, brute force:
2  2  3   6   6  (also - no solutions found for 4 fractions)

        program cub

        implicit none

        integer i1,i2,i3,i4,i5,itol,itop,itell

        real x1,x2,x3,x4,x5,a2,a3,a4,sum,tt,err

        itell=10

        tt=2./3.

        itop=200

        itol=6

        err=10.**(-itol)

          do 1 i1=2,itop

          if((i1/itell)*itell.eq.i1)print*,i1, 'out of ',itop

          x1=1./i1**2

            do 2 i2=2,itop

            x2=1./i2**2

            a2=x1+x2

            if(a2.gt.tt) go to 2

              do 3 i3=2,itop

              x3=1./i3**2

              a3=a2+x3

              if(a3.gt.tt)go to 3

                do 4 i4=1,itop

                x4=1./i4**2

                a4=a3+x4

                if(a4.gt.tt)go to 4

                  do 5 i5=2,itop

                  x5=1./i5**2

                  sum=a4+x5

                  if(sum.gt.tt)go to 5

                  if(abs(sum-tt).lt.err)then

                  print*,i1,i2,i3,i4,i5

                  stop

                  endif

5                 enddo

4               enddo

3             enddo

2           enddo

1         enddo

        end

Edited on August 25, 2020, 10:05 am
  Posted by Steven Lord on 2020-08-25 09:56:07

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